Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:296AD2of2 GHM
Order: 20
Horizontal side: 296 Vertical side: 296
Elements: 8, 8√2, 16, 16√2, 28, 32, 23√2, 28√2, 32√2, 46, 37√2, 46√2, 74, 56√2, 74√2, 120, 148, 111√2, 125√2, 148√2.
Code: 1485 0 148 1484 148 148 1256 171 171 230 171 171 742 74 74 741 74 148 372 111 111 1201 194 148 562 250 92 1110 111 111 326 218 60 462 296 46 166 202 44 325 218 28 463 296 0 86 194 36 165 202 28 85 194 28 284 222 0 283 250 0
The properties below may precede order:side in a tiling's title:
- c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
- d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
- e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
- i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
- r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.
Credit for Discovery
Just three people are credited with the discovery of Primitive Perfects:
Geoffrey H. Morley (GHM, England)
Jasper D. Skinner, II (JDS, United States)
William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)